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  3. A country’s per capita national debt is its national debt divided by its population．Is the per capita national debt of Country G

A country’s per capita national debt is its national debt divided by its population．Is the per capita national debt of Country G

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问题 A country’s per capita national debt is its national debt divided by its population．Is the per capita national debt of Country G within ＄5 of $500?
(1) Country G’s national debt to the nearest S1，000，000，000 is ＄43，000，000，000．
(2) Country G’s Population to the nearest 1，000，000 is 86．000，000．
选项 A、Statement(1) ALONE is sufficient，but statement (2) alone is not sufficient．
B、Statement(2) ALONE is sufficient，but statement (1) alone is not sufficient．
C、BOTH statements TOGETHER are sufficient，but NEITHER statement ALONE is sufficient．
D、EACH statement ALONE is sufficient．
E、Statements(1) and(2) TOGETHER are NOT sufficient．
答案E
解析 Briefly, the question is whether 495≤debt/population ≤505 is true.
(1)     We are given that 42.5 billion ≤ debt < 43.5 billion. However, no information is given about the population; NOT sufficient.
(2)     We are given that 85.5 million ≤ population < 86.5 million. However, no information is given about the debt; NOT sufficient.
Given (1) and (2), then to determine whether debt/population lies between 495 and 505, we will investigate the minimum possible value of debt/population and the maximum possible value of debt/population. To simplify the discussion that follows, we will assume that the upper bounds given in (1) and (2) can be achieved. This will not affect our conclusions because with this assumption, the estimates we obtain will still justify our conclusions. The minimum possible value of debt/population is minimum debt/maximum population=42.5 billion /86.5 million=(42.5/86.5)×1000.
Since ，which is less than ，it follows that the minimum possible value of debt/population is less than (1/2-1/200)×1,000 = 500 - 5 = 495.                    
The maximum possible value of debt/population is maximum debt/minimum population=43.5billon/85.5millon=(43.5/85.5)×1000.
since , which is greater than , it follows that the maximum possible value of debt/population is greater than (1/2-1/200) = 500 + 5 = 505.               
Since the minimum possible value of debt/population is less than 495 and the maximum possible value of debt/population is greater than 505, it is not possible to determine whether or not debt/population lies between 495 and 505.
The correct answer is E;
both statements together are still not sufficient.
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